aspg-21-2231-1791475965 20261008161245 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 Ahmedia Musa M. Ibrahim Department of Business Administration, College of Sciences and the Human Sciences in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia Zahid Khan Department of Quantitative Methods, Pannon Egyetem, Veszprem, H-8200, Hungary This paper introduces the concept of the neutrosophic Laplace distribution ( style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>L 10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>D 10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> m:val="p"/>N ), a probability distribution derived from the Laplace distribution. The style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>L 10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>D 10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> m:val="p"/>N offers a versatile framework for describing various real-world problems. We highlight the neutrosophic extension of the Laplace distribution and explore its applications in different areas. Extensive investigations into the mathematical properties of the distribution are presented, including the derivation of its probability density function, mean, variance, raw moment, skewness, and kurtosis. To estimate the parameters of the style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/> L 10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>D 10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> m:val="p"/>N , we employ the method of maximum likelihood (ML) estimation within a neutrosophic environment. Furthermore, we conduct a simulation study to assess the effectiveness of the maximum likelihood approach in estimating the parameters of this new distribution. The findings demonstrate the potential of the font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'>L style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>D 10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> m:val="p"/>N in modeling and analyzing real-world phenomena. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems. 2024 73 84 2231 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230106 https://www.americaspg.com/journal/21/article/2231 https://www.americaspg.com/storage/01699967948.pdf